Glasnik Matematicki, Vol. 47, No. 1 (2012), 95-104.

ON FUNCTIONAL EQUATIONS RELATED TO DERIVATIONS IN SEMIPRIME RINGS AND STANDARD OPERATOR ALGEBRAS

Nejc Širovnik

Department of Mathematics and Computer Science, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, 2000 Maribor, Slovenia
e-mail: nejc.sirovnik@uni-mb.si


Abstract.   In this paper functional equations related to derivations on semiprime rings and standard operator algebras are investigated. We prove, for example, the following result, which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators of X into itself and let A(X) ⊂ L(X) be a standard operator algebra. Suppose there exist linear mappings D,G:A(X) → L(X) satisfying the relations D(A3)=D(A2)A+A2G(A),G(A3)=G(A2)A+A2D(A) for all A A(X). In this case there exists B L(X) such that D(A)=G(A)=[A,B] holds for all A A(X).

2010 Mathematics Subject Classification.   16N60, 46B99, 39B42.

Key words and phrases.   Prime ring, semiprime ring, Banach space, standard operator algebra, derivation, Jordan derivation, Jordan triple derivation.


Full text (PDF) (free access)

DOI: 10.3336/gm.47.1.07


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